The various performance criteria applied in this analysis include the probability of reaching the ultimate target, the costs, elapsed times and system vulnerability resulting from any intrusion. This Excel file contains all the logical, probabilistic and statistical data entered by a user, and required for the evaluation of the criteria. It also reports the results of all the computations.

This Excel table contains a detailed example of a graph-theoretic model used in the specification of the physical topology and network of the modeled system.

This data release includes water-quality data collected at 38 sites in central and eastern Massachusetts from April 2018 through May 2019 by the U.S. Geological Survey to support the implementation of site-dependent aluminum criteria for Massachusetts waters. Samples of effluent and receiving surface waters were collected monthly at four wastewater-treatment facilities (WWTFs) and seven water-treatment facilities (WTFs) (see SWQ_data_and_instantaneous_CMC_CCC_values.txt). The measured properties and constituents include pH, hardness, and filtered (dissolved) organic carbon, which are required inputs to the U.S. Environmental Protection Agency's Aluminum Criteria Calculator version 2.0. Outputs from the Aluminum Criteria Calculator are also provided in that file; these outputs consist of acute (Criterion Maximum Concentration, CMC) and chronic (Criterion Continuous Concentration, CCC) instantaneous water-quality values for total recoverable aluminum, calculated for monthly samples at selected ambient sites near each of the 11 facilities. Quality-control data from blank, replicate, and spike samples are provided (see SWQ_QC_data.txt). In addition to data tables, the data release includes time-series graphs of the discrete water-quality data (see SWQ_plot_discrete_all.zip). For pH, time-series graphs also are provided showing pH from the discrete monthly water-quality samples as well as near-continuous pH measured at one surface-water site at each facility (see SWQ_plot_contin_discrete_pH.zip). The near-continuous pH data, along with all of the discrete water-quality data except the quality-control data, are also available online from the U.S. Geological Survey's National Water Information System (NWIS) database (https://nwis.waterdata.usgs.gov/nwis).

This thesis investigates the parameterized computational complexity of six classic graph problems lifted to a temporal setting. More specifically, we consider problems defined on temporal graphs, that is, a graph where the edge set may change over a discrete time interval, while the vertex set remains unchanged. Temporal graphs are well-suited to model dynamic data and hence they are naturally motivated in contexts where dynamic changes or time-dependent interactions play an important role, such as, for example, communication networks, social networks, or physical proximity networks. The most important selection criteria for our problems was that they are well-motivated in the context of dynamic data analysis. Since temporal graphs are mathematically more complex than static graphs, it is maybe not surprising that all problems we consider in this thesis are NP-hard. We focus on the development of exact algorithms, where our goal is to obtain fixed-parameter tractability results, and refined computational hardness reductions that either show NP-hardness for very restricted input instances or parameterized hardness with respect to “large” parameters. In the context of temporal graphs, we mostly consider structural parameters of the underlying graph, that is, the graph obtained by ignoring all time information. However, we also consider parameters of other types, such as ones trying to measure how fast the temporal graph changes over time. In the following we briefly discuss the problem setting and the main results. Restless Temporal Paths. A path in a temporal graph has to respect causality, or time, which means that the edges used by a temporal path have to appear at non-decreasing times. We investigate temporal paths that additionally have a maximum waiting time in every vertex of the temporal graph. Our main contributions are establishing NP-hardness for the problem of finding restless temporal paths even in very restricted cases, and showing W[1]-hardness with respect to the feedback vertex number of the underlying graph. Temporal Separators. A temporal separator is a vertex set that, when removed from the temporal graph, destroys all temporal paths between two dedicated vertices. Our contribution here is twofold: Firstly, we investigate the computational complexity of finding temporal separators in temporal unit interval graphs, a generalization of unit interval graphs to the temporal setting. We show that the problem is NP-hard on temporal unit interval graphs but we identify an additional restriction which makes the problem solvable in polynomial time. We use the latter result to develop a fixed-parameter algorithm with a “distance-to-triviality” parameterization. Secondly, we show that finding temporal separators that destroy all restless temporal paths is Σ-P-2-hard. Temporal Matchings. We introduce a model for matchings in temporal graphs, where, if two vertices are matched at some point in time, then they have to “recharge” afterwards, meaning that they cannot be matched again for a certain number of time steps. In our main result we employ temporal line graphs to show that finding matchings is NP-hard even on instances where the underlying graph is a path. Temporal Coloring. We lift the classic graph coloring problem to the temporal setting. In our model, every edge has to be colored properly (that is, the endpoints are colored differently) at least once in every time interval of a certain length. We show that this problem is NP-hard in very restricted cases, even if we only have two colors. We present simple exponential-time algorithms to solve this problem. As a main contribution, we show that these algorithms presumably cannot be improved significantly. Temporal Cliques and s-Plexes. We propose a model for temporal s-plexes that is a canonical generalization of an existing model for temporal cliques. Our main contribution is a fixed-parameter algorithm that enumerates all maximal temporal s-plexes in a given temporal graph, where we use a temporal adaptation of degeneracy as a parameter. Temporal Cluster Editing. We present a model for cluster editing in temporal graphs, where we want to edit all “layers” of a temporal graph into cluster graphs that are sufficiently similar. Our main contribution is a fixed-parameter algorithm with respect to the parameter “number of edge modifications” plus the “measure of similarity” of the resulting clusterings. We further show that there is an efficient preprocessing procedure that can provably reduce the size of the input instance to be independent of the number of vertices of the original input instance.

Using the User Manual included in the research paper, and the Graph Design Example file as a reference, the user enters or saves all the vertices and edges needed to specify the model of the system topography.

Various datasets from the Bayesys repository.

Size: 6 groups of datasets with each up to 16 experimentally generated from the bayesian network with the number of observation 100,1000,…100000. Ground truth is given

Number of features: 6 - over 1000

Ground truth: Yes

Type of Graph: Directed graph

Six discrete BN case studies are used to generate data. The first three of them represent well-established examples from the BN structure learning literature, whereas the other three represent new cases and are based on recent BN real-world applications. Specifically,

Asia: A small toy network for diagnosing patients at a clinic;

Alarm: A medium-sized network based on an alarm message system for patient monitoring;

Pathfinder: A very large network that was designed to assist surgical pathologists with the diagnosis of lymph-node diseases;

Sports: A small BN that combines football team ratings with various team performance statistics to predict a series of match outcomes;

ForMed: A large BN that captures the risk of violent reoffending of mentally ill prisoners, along with multiple interventions for managing this risk;

Property: A medium BN that assesses investment decisions in the UK property market.

Data generated with noise:

Synthetic datasets - noise


    Experiment No.
    Experiment
    Notes




    1
    N
    No noise


    2
    M5
    Missing data (5%)


    3
    M10
    Missing data (10%)


    4
    I5
    Incorrect data (5%)


    5
    I10
    Incorrect data (10%)


    6
    S5
    Merged states data (5%)


    7
    S10
    Merged states data (10%)


    8
    L5
    Latent confounders (5%)


    9
    L10
    Latent confounders (10%)


    10
    cMI
    M5 and I5


    11
    cMS
    M5 and S5


    12
    cML
    M5 and L5


    13
    cIS
    I5 and S5


    14
    cIL
    I5 and L5


    15
    cSL
    S5 and L5


    16
    cMISL
    M5, I5, S5 and L5

More information about the datasets is contained in the dataset_description.html files.

We propose a stochastic generative model to represent a directed graph constructed by citations among academic papers, where nodes and directed edges represent papers with discrete publication time and citations respectively. The proposed model assumes that a citation between two papers occurs with a probability based on the type of the citing paper, the importance of cited paper, and the difference between their publication times, like the existing models. We consider the out-degrees of citing paper as its type, because, for example, survey paper cites many papers. We approximate the importance of a cited paper by its in-degrees. In our model, we adopt three functions: a logistic function for illustrating the numbers of papers published in discrete time, an inverse Gaussian probability distribution function to express the aging effect based on the difference between publication times, and an exponential distribution (or a generalized Pareto distribution) for describing the out-degree distribution. We consider that our model is a more reasonable and appropriate stochastic model than other existing models and can perform complete simulations without using original data. In this paper, we first use the Web of Science database and see the features used in our model. By using the proposed model, we can generate simulated graphs and demonstrate that they are similar to the original data concerning the in- and out-degree distributions, and node triangle participation. In addition, we analyze two other citation networks derived from physics papers in the arXiv database and verify the effectiveness of the model. Methods We focus on a subset of the Web of Science (WoS), WoS-Stat, which is a citation network that comprises the citations between papers published in journals whose subject is associated with “Statistics and Probability.” We construct a citation network utilizing a paper identifier (ID), publication year, and reference list (list of paper IDs) for 36 years, from 1981 to 2016. WoS-Stat consists of 179,483 papers and 1,106,622 citations.

High-throughput technologies have led to the generation of an increasing amount of data in different areas of biology. Datasets capturing the cell’s response to its intra- and extra-cellular microenvironment allows such data to be incorporated as signed and directed graphs or influence networks. These prior knowledge networks (PKNs) represent our current knowledge of the causality of cellular signal transduction. New signalling data is often examined and interpreted in conjunction with PKNs. However, different biological contexts, such as cell type or disease states, may have distinct variants of signalling pathways, resulting in the misinterpretation of new data. The identification of inconsistencies between measured data and signalling topologies, as well as the training of PKNs using context specific datasets (PKN contextualization), are necessary conditions to construct reliable, predictive models, which are current challenges in the systems biology of cell signalling. Here we present PRUNET, a user-friendly software tool designed to address the contextualization of a PKNs to specific experimental conditions. As the input, the algorithm takes a PKN and the expression profile of two given stable steady states or cellular phenotypes. The PKN is iteratively pruned using an evolutionary algorithm to perform an optimization process. This optimization rests in a match between predicted attractors in a discrete logic model (Boolean) and a Booleanized representation of the phenotypes, within a population of alternative subnetworks that evolves iteratively. We validated the algorithm applying PRUNET to four biological examples and using the resulting contextualized networks to predict missing expression values and to simulate well-characterized perturbations. PRUNET constitutes a tool for the automatic curation of a PKN to make it suitable for describing biological processes under particular experimental conditions. The general applicability of the implemented algorithm makes PRUNET suitable for a variety of biological processes, for instance cellular reprogramming or transitions between healthy and disease states.

Table 1 - Discrete Logic Modelling Optimization to Contextualize Prior Knowledge Networks Using PRUNET

This study addresses the problem of attack identification in discrete event systems modeled with Petri nets, focusing specifically on sensor attacks that mislead observers to making incorrect decisions. Insertion attacks are one of the sensor attacks that are considered in this work. First, we formulate a novel observation structure to systematically model insertion attacks within the Petri net framework. Second, by generating an extended reachability graph that incorporates the observation structure, we can find a special class of markings whose components can have negative markings. Third, an observation place is computed by formulating an integer linear programming problem, enabling precise detection of attack occurrences. The occurrence of an attack can be identified by the number of tokens in the designed observation place. Finally, examples are provided to verify the proposed approach. Comparative analysis with existing techniques demonstrates that the reported approach offers enhanced detection accuracy and robustness, making it a significant advancement in the field of secure discrete event systems.

This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions in space and time, potentially resulting in differences in network structure among groups. Therefore, the iid assumption is unrealistic, and fitting a single graphical model on all data results in a network that does not accurately represent the between group differences. In addition, real-world observational data is typically of mixed discrete-and-continuous type, violating the Gaussian assumption that is typical of graphical models, which leads to the model being unable to adequately recover the underlying graph structure. Both these problems are solved by fitting a different graph for each group, applying the fused group penalty to fuse similar graphs together and by treating the observed data as transformed latent Gaussian data, respectively. The proposed model outperforms related models on learning partial correlations in a simulation study. Finally, the proposed model is applied on real on-farm maize yield data, showcasing the added value of the proposed method in generating new production-ecological hypotheses. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=heteromixgm. Supplementary materials for this article are available online.